The easy stuff first.The link on the fourseasons.com is not coded correctly. They have the address of your site, but the underlying link is:http://taste.fourseasons.com/2013/03/48-hours-in-paris-cruising-the-cookbook-fair-and-sipping-tea-at-the-george-v/www.annekleinberg.com.
It should be: http://www.annekleinberg.com
As for the upgrade, it does not look like the Magazine Basic theme as changed that much and from the outside it does not appear that you have that many plugins installed, so chance are that nothing negative will happen when you update and you should update for he reasons I noted previously.
For peace of mind you should have a backup of your site and database. GoDaddy does not appear to offer any easy method for doing this. For someone who describes herself as a "disaster at back-end stuff" I would recommend using the following plugin: WordPress Backup for Dropbox (http://wordpress.org/support/view/plugin-reviews/wordpress-backup-to-dropbox).
It is a popular plugin, well documented and supported. There are also instructions for restoring your site. You do need a Dropbox account, but you can get a free one and it should be sufficient for your site.
There is a similar plugin for Google Drive, but it is not as popular or well documented:http://wordpress.org/extend/plugins/wp-google-drive/